相关论文: Localization-delocalization phenomena for random i…
We consider random walks evolving on two models of connected and undirected graphs and study the exact large deviations of a local dynamical observable. We prove, in the thermodynamic limit, that this observable undergoes a first-order…
We consider localization of a random walk (RW) when attracted or repelled by multiple extended manifolds of different dimensionalities. In particular, we focus on $(d-1)$- and $(d-2)$-dimensional manifolds in $d$-dimensional space, where…
The scaling properties of a random walker subject to the global constraint that it needs to visit each site an even number of times are determined. Such walks are realized in the equilibrium state of one dimensional surfaces that are…
We survey recent results on some one- and two-dimensional patterns generated by random permutations of natural numbers. In the first part, we discuss properties of random walks, evolving on a one-dimensional regular lattice in discrete time…
Locally activated random walks are defined as random processes, whose dynamical parameters are modified upon visits to given activation sites. Such dynamics naturally emerge in living systems as varied as immune and cancer cells interacting…
We study a symmetric random walk (RW) in one spatial dimension in environment, formed by several zones of finite width, where the probability of transition between two neighboring points and corresponding diffusion coefficient are…
The probabilistic study of effective interface models has been quite active in recent years, with a particular emphasis on the effect of various external potentials (wall, pinning potential, ...) leading to localization/delocalization…
A recently developed model of random walks on a $D$-dimensional hyperspherical lattice, where $D$ is {\sl not} restricted to integer values, is extended to include the possibility of creating and annihilating random walkers. Steady-state…
We consider connectivity properties of certain i.i.d. random environments on $\Z^d$, where at each location some steps may not be available. Site percolation and oriented percolation can be viewed as special cases of the models we consider.…
The symmetries associated with discrete-time quantum walks (DTQWs) and the flexibilities in controlling their dynamical parameters allow to create a large number of topological phases. An interface in position space, which separates two…
After a general introduction to the field, we describe some recent results concerning disorder effects on both `random walk models', where the random walk is a dynamical process generated by local transition rules, and on `polymer models',…
Modeling of polymer chains has received a lot of attention in mathematics. In fact, probabilistic models that naturally arise in statistical mechanics have been widely studied by mathematicians for the very challenging and novel problems…
In these proceedings, we first summarize some general properties of phase transitions in the presence of quenched disorder, with emphasis on the following points: the need to distinguish typical and averaged correlations, the possible…
We study the localisation of lattice polymer models near a permeable interface in two dimensions. Localisation can arise due to an interaction between the polymer and the interface, and can be altered by a preference for the bulk solvent on…
These notes are devoted to the statistical mechanics of directed polymers interacting with one-dimensional spatial defects. We are interested in particular in the situation where frozen disorder is present. These polymer models undergo a…
We study, on a $d$ dimensional hypercubic lattice, a random walk which is homogeneous except for one site. Instead of visiting this site, the walker hops over it with arbitrary rates. The probability distribution of this walk and the…
We consider random walk on a mildly random environment on finite transitive d- regular graphs of increasing girth. After scaling and centering, the analytic spectrum of the transition matrix converges in distribution to a Gaussian noise. An…
We study "random surfaces," which are random real (or integer) valued functions on Z^d. The laws are determined by convex, nearest neighbor, difference potentials that are invariant under translation by a full-rank sublattice L of Z^d; they…
We explore some of the connections between the local picture left by the trace of simple random walk on a discrete cylinder with base a d-dimensional torus, d at least 2, of side-length N running for times of order N^{2d} and the model of…
We introduce the notion of \emph{localization at the boundary} for conditioned random walks in i.i.d. and uniformly elliptic random environment on $\mathbb{Z}^d$, in dimensions two and higher. Informally, this means that the walk spends a…